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The centralizer of a classical group and Bruhat-Tits buildings

Daniel Skodlerack (2013)

Annales de l’institut Fourier

Let G be a unitary group defined over a non-Archimedean local field of odd residue characteristic and let H be the centralizer of a semisimple rational Lie algebra element of G . We prove that the Bruhat-Tits building 𝔅 1 ( H ) of H can be affinely and G -equivariantly embedded in the Bruhat-Tits building 𝔅 1 ( G ) of G so that the Moy-Prasad filtrations are preserved. The latter property forces uniqueness in the following way. Let j and j ′ be maps from 𝔅 1 ( H ) to 𝔅 1 ( G ) which preserve the Moy–Prasad filtrations. We prove that...

The circle method and pairs of quadratic forms

Henryk Iwaniec, Ritabrata Munshi (2010)

Journal de Théorie des Nombres de Bordeaux

We give non-trivial upper bounds for the number of integral solutions, of given size, of a system of two quadratic form equations in five variables.

The connection between quadratic forms and the extended modular group

Ahmet Tekcan, Osman Bizim (2003)

Mathematica Bohemica

In this paper some properties of quadratic forms whose base points lie in the point set F Π ¯ , the fundamental domain of the modular group, and transforming these forms into the reduced forms with the same discriminant Δ < 0 are given.

The image of the natural homomorphism of Witt rings of orders in a global field

Beata Rothkegel (2013)

Acta Arithmetica

Let R be a Dedekind domain whose field of fractions is a global field. Moreover, let 𝓞 < R be an order. We examine the image of the natural homomorphism φ : W𝓞 → WR of the corresponding Witt rings. We formulate necessary and sufficient conditions for the surjectivity of φ in the case of all nonreal quadratic number fields, all real quadratic number fields K such that -1 is a norm in the extension K/ℚ, and all quadratic function fields.

Currently displaying 921 – 940 of 1236